Abstract
Electrostatic interactions among colloidal particles are often described using the venerable (two-particle) Derjaguin–Landau–Verwey–Overbeek (DLVO) approximation and its various modifications. However, until the recent development of a many-body theory exact at the Debye–Hückel level (Yu in Phys Rev E 102:052404, 2020), it was difficult to assess the errors of such approximations and impossible to assess the role of many-body effects. By applying the exact Debye–Hückel level theory, we quantify the errors inherent to DLVO and the additional errors associated with replacing many-particle interactions by the sum of pairwise interactions (even when the latter are calculated exactly). In particular, we show that: (1) the DLVO approximation does not provide sufficient accuracy at shorter distances, especially when there is an asymmetry in charges and/or sizes of interacting dielectric spheres; (2) the pairwise approximation leads to significant errors at shorter distances and at large and moderate Debye lengths and also gets worse with increasing asymmetry in the size of the spheres or magnitude or placement of the charges. We also demonstrate that asymmetric dielectric screening, i.e., the enhanced repulsion between charged dielectric bodies immersed in media with high dielectric constant, is preserved in the presence of free ions in the medium.Graphic abstract
Highlights
The search for methods providing more accurate descriptions and deeper understanding of electrostatic interactions among charged dielectric spheres in ionic solutions remains, despite its long history, a subject of high interest, as proven by a persistent stream of theoretical and experimental publications. This continued interest is motivated by new types of dielectric objects that could be approximated by dielectric spheres and whose properties and interactions are important for other fields of physics, chemistry, materials design and biology
It is commonly accepted that, under not too extreme circumstances, each ion in the ionic solution can be considered freely diffusing through the solution in a canonically averaged electric potential φ(r), created by an “atmosphere” of other free ions and ionized colloidal particles
We provide a two-dimensional cross-sectional view of the strength of the potential for the spheres separated by 250 nm, which ranges from approximately 0.11 kBT to 0.02 kBT ods [29], integral equation methods [30], expansions of induced surface charges into a series of polynomials [31], solving the Poisson equations in specialized coordinate systems [32], discretization of dielectric surfaces aimed at finding numerical solutions for arbitrary geometries [33,34], direct numerical solution of differential equations [35,36], and so-called hybrid methods [37]
Summary
The search for methods providing more accurate descriptions and deeper understanding of electrostatic interactions among charged dielectric spheres in ionic solutions remains, despite its long history, a subject of high interest, as proven by a persistent stream of theoretical and experimental publications. Among the methods using the Debye–Huckel theory and employing an expansion of surface charge into a polynomial series and using the boundary conditions to find the expansion coefficients of such series, we should highlight the rigorous formalism of Fisher et al [9] They devised a set of polynomials to serve as the basis set of the expansion and were able to solve the boundary value problem for two identical spheres in an electrolyte solution with either like or opposite point charges at their centers, thereby obtaining an expression for the interaction energy. The most recent work [39] contains a general formalism, rigorous within the Debye–Huckel approximation, for describing interactions among dielectric spheres immersed in an electrolyte solution. We illustrate how the speed of convergence depends on variation of radii, charge magnitude and charge placement in the system
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
